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185
Pseudorandom generators for spacebounded computation
 Combinatorica
, 1992
"... Pseudorandom generators are constructed which convert O(SlogR) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). In particular, any randomized polynomial time algorithm that runs in space S can be simulated using only O(Slogn) random bits. An application of these ..."
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Cited by 192 (10 self)
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Pseudorandom generators are constructed which convert O(SlogR) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). In particular, any randomized polynomial time algorithm that runs in space S can be simulated using only O(Slogn) random bits. An application of these generators is an explicit construction of universal traversal sequences (for arbitrary graphs) of length n O(l~ The generators constructed are technically stronger than just appearing random to spacebounded machines, and have several other applications. In particular, applications are given for "deterministic amplification " (i.e. reducing the probability of error of randomized algorithms), as well as generalizations of it. 1.
Random Walks in PeertoPeer Networks
, 2004
"... We quantify the effectiveness of random walks for searching and construction of unstructured peertopeer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of reissuing the same request several tim ..."
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Cited by 178 (2 self)
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We quantify the effectiveness of random walks for searching and construction of unstructured peertopeer (P2P) networks. For searching, we argue that random walks achieve improvement over flooding in the case of clustered overlay topologies and in the case of reissuing the same request several times. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is bounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.
Efficient probabilistically checkable proofs and applications to approximation
 In Proceedings of STOC93
, 1993
"... 1 ..."
Signature Schemes Based on the Strong RSA Assumption
 ACM TRANSACTIONS ON INFORMATION AND SYSTEM SECURITY
, 1998
"... We describe and analyze a new digital signature scheme. The new scheme is quite efficient, does not require the the signer to maintain any state, and can be proven secure against adaptive chosen message attack under a reasonable intractability assumption, the socalled Strong RSA Assumption. Moreove ..."
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Cited by 154 (8 self)
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We describe and analyze a new digital signature scheme. The new scheme is quite efficient, does not require the the signer to maintain any state, and can be proven secure against adaptive chosen message attack under a reasonable intractability assumption, the socalled Strong RSA Assumption. Moreover, a hash function can be incorporated into the scheme in such a way that it is also secure in the random oracle model under the standard RSA Assumption.
Numbertheoretic constructions of efficient pseudorandom functions
 In 38th Annual Symposium on Foundations of Computer Science
, 1997
"... ..."
Sequences of Games: A Tool for Taming Complexity in Security Proofs
, 2004
"... This paper is brief tutorial on a technique for structuring security proofs as sequences games. ..."
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Cited by 116 (0 self)
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This paper is brief tutorial on a technique for structuring security proofs as sequences games.
Construction of asymptotically good, lowrate errorcorrecting codes through pseudorandom graphs
 IEEE Transactions on Information Theory
, 1992
"... A new technique, based on the pseudorandom properties of certain graphs, known as expanders, is used to obtain new simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling and then regrouping ..."
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Cited by 116 (22 self)
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A new technique, based on the pseudorandom properties of certain graphs, known as expanders, is used to obtain new simple explicit constructions of asymptotically good codes. In one of the constructions, the expanders are used to enhance Justesen codes by replicating, shuffling and then regrouping the code coordinates. For any fixed (small) rate, and for sufficiently large alphabet, the codes thus obtained lie above the Zyablov bound. Using these codes as outer codes in a concatenated scheme, a second asymptotic good construction is obtained which applies to small alphabets (say, GF (2)) as well. Although these concatenated codes lie below Zyablov bound, they are still superior to previouslyknown explicit constructions in the zerorate neighborhood.
Simulating BPP Using a General Weak Random Source
 ALGORITHMICA
, 1996
"... We show how to simulate BPP and approximation algorithms in polynomial time using the output from a ffisource. A ffisource is a weak random source that is asked only once for R bits, and must output an Rbit string according to some distribution that places probability no more than 2 \GammaffiR on ..."
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Cited by 111 (18 self)
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We show how to simulate BPP and approximation algorithms in polynomial time using the output from a ffisource. A ffisource is a weak random source that is asked only once for R bits, and must output an Rbit string according to some distribution that places probability no more than 2 \GammaffiR on any particular string. We also give an application to the unapproximability of Max Clique.
Dispersers, Deterministic Amplification, and Weak Random Sources.
, 1989
"... We use a certain type of expanding bipartite graphs, called disperser graphs, to design procedures for picking highly correlated samples from a finite set, with the property that the probability of hitting any sufficiently large subset is high. These procedures require a relatively small number of r ..."
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Cited by 94 (12 self)
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We use a certain type of expanding bipartite graphs, called disperser graphs, to design procedures for picking highly correlated samples from a finite set, with the property that the probability of hitting any sufficiently large subset is high. These procedures require a relatively small number of random bits and are robust with respect to the quality of the random bits. Using these sampling procedures to sample random inputs of polynomial time probabilistic algorithms, we can simulate the performance of some probabilistic algorithms with less random bits or with low quality random bits. We obtain the following results: 1. The error probability of an RP or BPP algorithm that operates with a constant error bound and requires n random bits, can be made exponentially small (i.e. 2 \Gamman ), with only (3 + ffl)n random bits, as opposed to standard amplification techniques that require \Omega\Gamma n 2 ) random bits for the same task. This result is nearly optimal, since the informati...